One may wonder if this apparently simplistic definition induces some actually sensible behavioral equivalence. The first main contribution of this paper is to show that, surprisingly enough,
net bisimilarity \(\sim _n\)  coincides with a well-known, truly-concurrent behavioral relation, proposed some years ago by R. van Glabbeek,
namely structure-preserving bisimilarity [1]}
or, equivalently, causal-net bisimilarity [1]}, [3]}, whose decidability on unbounded Petri nets is an open problem and which is
intuitively very appealing. Causal-net bisimilarity \(\sim _{cn}\)  is essentially a bisimulation-like relation over the
causal nets (sometimes called nonsequential processes) [4]}, [5]}, [6]} originating from
the two initial markings of interest. Hence, as net bisimilarity coincides with causal-net bisimilarity, we get that our extremely simple definition
of net bisimilarity
is slightly finer than fully-concurrent bisimilarity [7]} in that it
relates markings that not only generate the same the partial orders of events, but that also have the same size.
